Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation: III. Hollow columns and plates
Journal of Geophysical Research: Atmospheres
 The ability of an assembly of spheres to represent scattering and absorption by a nonspherical ice crystal of the same volume-to-area (V/A) ratio was previously evaluated for convex shapes (circular cylinders and hexagonal prisms). Here we extend the comparison to indented and hollow prisms, which are common in ice clouds. In the equivalent-sphere representation, the crystal mass and surface area are both conserved. Internal surfaces as well as external surfaces contribute to the total surface area; in the model representation both become external surfaces of spheres. The optical depth ? of the model cloud is thus greater than that of the real cloud by the ratio A/4P, where A is the total area of the nonspherical particle and P is the orientation-averaged projected area. This ratio, which we call “fluffiness,” is unity for convex shapes but may exceed 2 for clusters of hollow bullets. In effect, the scattering at interior surfaces of a hollow crystal becomes classified as multiple scattering in the model of ice spheres. Therefore, rather than directly comparing the asymmetry factor (g) and single-scattering albedo (?o) of the hollow crystal to those of the equal-V/A sphere, it is more appropriate to compare the product ?(1 ? g)?o, because this quantity largely determines the bulk radiative properties of the cloud. Errors in albedo, absorptance, and transmittance of ice clouds, caused by the equal-V/A representation, are presented for a range of aspect ratios, indentation depths, and ice-water paths at visible and near-infrared wavelengths.
Grenfell, T. C., S. P. Neshyba, and S. G. Warren. 2005. "Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation: 3. Hollow columns and plates (DOI 10.1029/2005JD005811)". Journal of Geophysical Research. 110 (D17): D17203.